Greece’s travails may threaten to deconstruct the euro, but its guardians now have a new headquarters designed by an original master of deconstructivism. In Frankfurt, Coop Himmelb(l)au has housed The European Central Bank in twisting towers, and intervened in a vast historic market hall.

Out on the eastern edge of Frankfurt, where residential streets surrendered to rail, wharves and industry, the world's largest reinforced concrete structure of its time was completed in 1928. Designed by municipal architect Martin Elsaesser, the Grossmarkthalle was a market hall 220m long and 50m wide, bookended by eight-storey, solid, modernist, brick towers. Now, jagged not-quite-twin towers of not-quite-flat glass, linked through atria and stabilised by connecting steel, rise into the sky with glacial serenity beside the restored Weimar Republic behemoth. Through the market hall's northern facade, another angular form thrusts out horizontally.

The ECB has two elements -- the 1928 Grossmarkthalle cut by a new entrance building volume (left), and the towers (right)

Cantilevering above the entrance, it presents a great warped window that simultaneously seems to observe your arrival, and swivel sideways, as if keeping an eye on other things. This is the new 184,000 sq m headquarters of the European Central Bank (ECB), the institution charged with maintaining the stability of the world's number two currency, the euro. The design competition was launched in 2002, construction began then stopped in 2008, restarted in 2010, and the costs and the ECB's staff numbers outgrew the original plan. Nevertheless, they started moving in in November, and 2,900 people now work here in this showcase project, the latest by Vienna-based practice Coop Himmelb(l)au.

Wolf Prix's sketches illustrate the concept of towers with special geometry above the box of the old market hall

'It's a functional sculpture,' says its 72-year-old principal and co-founder Wolf Prix, of the €1.3bn building. 'It enlarges the meaning of function - it's not just value engineering, the function is also to make an emotional statement.' Wearing a grey suit and his trademark white scarf, Prix is sitting in the ECB's expansive cafeteria, eager to talk. His sunglasses come in handy as daylight streams directly through the vast concrete grid of the southern facade of the restored Grossmarkthalle, into a space bounded by the vaulted ceiling 23m above, and a great sidewall formed by brick and windows in the old western tower.

Frankfurt's skyscrapers are the subject of the Skyward exhibition at Deutsches Architekturmuseum

Prix's 'emotional statement' is about Europe. 'The European project is the most important of our century. Our democratic society is in danger,' he declares, continuing: 'We have a parliament building in Brussels, it's boring. This building has a special Gestalt.' He has chosen the word that means form, but also gives an instant idea of the form's entirety. 'It's an imprint on the retina.'

The concave curvature of the southern facade, viewed from the east, behind a railway bridge over the river Main

In sound terms, Prix suggests Mozart's Jupiter Symphony, or the last movement of the previous Symphony No. 40, as the music that matches the whole building. Before we explore this gestalt or symphony of volumes, angles and some curves, we should ask: How did Prix come from being a playful iconoclast who once attracted attention walking barefoot through Basel inside a 4m-diameter balloon to demonstrate pneumatic structures (the Restless Sphere project, 1971), to being a global 'starchitect' (a word he uses) with offices from Los Angeles to Beijing, delivering billion-euro projects?

Stacked atria between the towers bring light in and reveal diagonal beams that provide structural stability

Prix studied at Vienna's Technical University, the Architectural Association, London, and LA's Southern California Institute of Architecture, and in 1968, he co-founded Coop Himmelb(l)au in Vienna. Himmel, bau and blau mean heaven, build and blue. Prix reveals that the name 'comes from Shakespeare, a dialogue in Hamlet' (the one that starts 'Do you see yonder cloud that's almost in shape of a camel?'). 'It's the idea of architecture changing like clouds.'

The platform on level 38 is more than a sky lobby for changing lifts, it's a hang-out with its own summer chairs and viewing platform

In a 1995 bulletin of his philosophy, Prix said, 'Clouds are symbols for rapidly changing states... Viewed in slow motion, the architecture of urban development could be compared with patches of clouds'. A 1968 project was even called The Cloud - an Archigram-ish concept for an elevated platform that could be moved into urban gaps and raised. Another early project, with practice co-founder Helmut Swiczinsky, underlines the drive to defy gravity: House with a Flying Roof (1973) was an art installation that suspended a domestic roof in the air. It has been his only London work.

The Grossmarkthalle's ceiling vault, concrete grid facade and the old west tower's brick define the café. The Restaurant is above, inside the new volume (left)

The Cloud philosophy statement went on to say that 'the notions of centre, axis and spatial sequence will have to be replaced by tangents, vectors and sequences of images'. The language is strikingly similar to Zaha Hadid's, and it's no coincidence that they were both cast onto the international stage by an exhibition called Deconstructivist Architecture in 1988 at MoMA.

Money talks in the Council Chamber atop the South Tower. The ceiling reveals Europe from a certain angle, a window reveals a glimps of central skyscrapers

It was curated by Philip Johnson, who 56 years earlier had co-curated the seminal Modern Architecture show there, and coined the term International Style. Again, Johnson nailed a movement, presenting deconstructivism as an emerging style, with roots in constructivism but 'subverting' perfection for 'the pleasures of unease'. And again, Johnson brought forth the key players - the others being Eisenman, Gehry, Koolhaas, Libeskind and Tschumi.

Looking north in the Entrance Building lobby, to the welcome desk. The Press Centre cantilevers over the Entrance

This elite group became the riposte against postmodernism, and Coop Himmelb(l)au's contributions were as striking as any. They include the vivid, red cubist part of the Groninger Museum (1994), the UFA Cinema Center, Dresden (1998), with its madly leaning glass element, and the apartment tower and intervention into old brick at Gasometer B, Vienna (2001).

In the eastern side of the Grossmarkthalle, the Conference Centre occupies a volume-within-a-volume, the top floors of which are seen within the truss

The swirling, curvy BMW Welt, Munich, and the angled, cantilevering planes of the Akron Art Museum, Ohio, were both completed in 2007. The surprise and pace of output seems to be accelerating. In 2014, Lyons' Musée des Confluences, a spectacular 190m-long structure that links two elemental forms, Cloud and Crystal, opened just weeks before the ECB.

As in Lyon, the ECB has two connected principle parts, the office high-rise (itself two connected structures, 185m and 165m high) and the 80m-long Entrance Building (not to be confused with a small, outlying gateway building with a wide, flat wing roof) that cuts across the Grossmarkthalle. Three of Elsaesser's 15 concrete-shell, barrel-vault roof sections, all postwar rebuilds, and a section of north and south facade, have been demolished to make way for it.

The Entrance Building cuts through the Grossmarkthalle's north facade, thrusting into a cantilever in which press conferences are held. The 1928 brick west tower (foreground) now includes the ECB library and fitness facilities.

The section of new glass frontage facing north is where you enter the almost airport-terminal-sized lobby, into which an angled, translucent block, three storeys high, touches down behind the reception desk, like the hull of a spaceship. Above is the Press Centre, its main room occupying the cantilever. The panelled ceiling there looks like silvery water just gently disturbed by wind, and a wide slice of northern light falls through a full-wall-width curved window.

90 per cent of double-glazed glass panels in the tower facades are the same, each with blinds in the gap. Natural ventilation is enabled by integrated slats. Atrium facades absorb just a tenth of incoming solar gain.

From the outside, it echoes the great forward-looking window of Coop Himmelb(l) au's House of Music in Aalborg (also finished in 2014), but here, the surface is three-dimensional, bending with double hyperbolic paraboloid curvature. The cantilever is supported by two concrete piloti which seem to nod to Le Corbusier, one recessed behind the entrance facade. (Prix confides that 'I like Corbusier more' than the 'cold' Mies.)

The Entrance Building's other, southern end opens into a four-storey atrium that is the hub connecting all the main building volumes. A semi-circular 'Loop' houses a bend of connecting passageways overhead. The towers are to the south.

A diagonal support beam penetrates the glass in the screen through which we enter the main length of the Grossmarkthalle to the east. It supports a great raised and inclined steel truss, which articulates to run parallel to the concrete grid screen of the old southern facade. Behind the truss is the conference centre, a building within a building, reached by climbing grand stairs flanked by channels of water flowing down over another gently fluid, metallic surface. Further along, up more stairs, a wide, airy terrace beside the conference entrance looks out into a space ending at the brickwork of the eastern bookend tower, now offices. Overhead, ten of the original 15 concrete-shell roof vaults repeat westwards to vanish back above the truss.

Looking up from ground floor into the lowest atrium, we see the base of the lowest platform between the towers.

Elsaesser's old building - its restored brick (bound with darker, vertical mortar to accentuate horizontality) and great stretches of grid facade and roof shell - and Prix's interventions - the thick, metal structure-work, leaning walls, terraces and steps - both play with materiality and a satisfying sense of sequence.

The old diagonal columns supporting the roof are even echoed in Prix's new angularity. The effect is serene and harmonious. The Grossmarkthalle has known darker days. The Nazis brought 10,000 Jews there, to be deported on trains to death camps. This will not be forgotten. A memorial will open in the basement, designed by KatzKaiser, with a minimal, solidly walled ramp descending to it from the grounds in the east.

View from the south across the river Main, revealing the interconnecting structure between Grossmarkthalle and towers

The towers beckon. More than anything else, they define the ECB headquarters. Essentially, they are two irregular, rhomboid slabs with concrete frames, between which 14 angled, steel cross-beams and four steel platforms span. The platforms are at levels 3, 15, 27 and 38, and they define a stack of three atria, the largest 60m high. Dropped for cost reasons, the original plan was for hanging gardens in the atria, enclosed in gently twisting tubes. Passing some pot plants dotted around on the ground level, Prix suggests dryly that 'exploded pieces of it are there'.

Prismatic towers such as the Shard or One World Trade Center are becoming commonplace, but as Prix says, 'this is a building with special geometry', characterised by 'HP (hyperbolic paraboloid) deformed surfaces'. Unike the Press Centre's, window panels are flat, but the towers' north and south facades have overall curvature. They are gently concave and twisting, over an epic scale, with an overhang reaching 12m. Prix explains that they are 'rational', because as the surface 'bends, it supports the shaping. This is very Himmelb(l)au'. The effect is crucial to the gestalt - 'it's going to (the) subconscious.'

Prix says the atria create a 'vertical city', because 'the platforms are forums for little civic meetings', adding that 'it's very functional'. Stepping out at level 38, this is indeed more than just a sky lobby for changing between the express lifts in the atria and local ones in the towers. Garden chairs are grouped, a coffee point is to hand, and shallow steps with languid turns rise to the glazing, so people can linger and behold the view.

Although the south tower's 43 storeys are two less than the north tower's, the pinnacle of the ECB's power is situated here. From level 39 are three floors where the Executive Board has private offices, and above that is the Council Chamber. The seating is arranged circularly, and the view looks across to the skyscraper cluster of the Financial Quarter to the west, a kilometre separating the high command of the euro currency from the citadels of commercial banking, dominated by Foster's Commerzbank tower. Board or council rooms atop skyscrapers reinforce the god-like power of their occupants, and simultaneously place their heads in the clouds.

Wolf Prix, co-founder and principal of Coop Himmelb(l)au

Here, the ceiling seems to do the latter -- across it, a field of parallel strips, each cut with a differently curved, lower edge, suggests another Himmelb(l)au cloud reference. But it holds a hidden image -- from a certain angle, you can see the shape of Europe in it. Prix still wants to draw your attention like he did on city streets when he was younger, but now he does so with shinier, stranger shapes demanding a bigger stage.

The latest Coop Himmelb(l)au buildings, especially those in China, are like structures on a sci-fi dreamscape, often silvery, organic forms like vast, alien beasts. The ECB headquarters is sober by comparison, even with its asymmetric, subversively curving towers. The project does play a more deconstructivist hand internally, but the biggest surprise is its interplay with Elsaesser's functionalist expressionism (old labels that are also apt for Coop Himmelb(l)au).

Prix warns young architects that, 'when you want to make free forms, you are forced to make constrained forms', but here are free forms within and around the constraint of the old market hall. Prix's visions are still outside of the box - and inside this one. The whole, the gestalt, works as a brilliantly precise and logical unified structure. Rather like Mozart's music.

At the ECB, Frankfurt, Coop Himmelb(l)au principal, Wolf Prix, sat down with Herbert Wright to talk about deconstructivism, China and fish, and also offered advice for young architects.

Blueprint: The architects in MoMA's 1988 Deconstructivist show (Gehry, Hadid, Koolhaas etc.) are now big international names. Do you all share anything else in common?Prix: Yes. We all depend in a similar way on our cultural background. Austrian architects are more dependent on baroque space sequences, lots of structure. They try to dissolve the structural constraints. If the architect is good, he tries to overcome gravity. Look at that LC4 (chair) by Le Corbusier -- if you lie there, you have the same position as astronauts taking off. This is not by chance. The Dutch guys like Rietveld are related to Calvinism, Jewish friends to Kabbalism.

Blueprint: In the UK, we had high-tech rather than deconstructivism - are they related?Prix: This is related to fish and chips, to farmers and sailors.

Who's driving? The Restless Sphere, demonstrated in Basel, 1971, was a 'transparent habitat' and also a 'means of transport'

Blueprint: Your architecture was once described as 'punk'.Prix: It is not punk, it's rock-and-roll.

Blueprint: Were you ever a rebel?Prix: No, never.

Blueprint: But do you accept the label 'deconstructivist'?Prix: Deconstructivism has a misunderstanding. People say it's connected with destroying. But (the word) deconstructivism comes from (French philosopher) Jacques Derrida. He proved that in a text, one word can unconsciously rule the whole understanding... Maybe Libeskind understood it. The architects who are neurotic, depressed, sexually infantile, they do buildings that are that way.

Blueprint: That sounds Freudian.Prix: Freud could only come up with his ideas in Vienna. Look at the (pompous neo-classical) buildings on Ringstrasse in Vienna. You can tell this society was preparing for World War One. What I can read from buildings is not just the elements, I read the society that puts these buildings. The problem of architectural theory is we only discuss the visible part. That's the tip of the iceberg. The invisible is the dangerous part. The design process is more like a whale than an iceberg.

A rendered robot fine grinds a welding seam on the Dolphin, within the MOCAPE, currently under construction in Shenzhen

Blueprint: What shapes Coop Himmelb(l)au design?Prix: (The German word) 'entwerfen' is at the root of our design. Each part throws up possibilities. 'Ent' comes from the unconscious, 'werfen' means 'throw'. The moment when you change from unconscious to conscious is when 30 tonnes can fly! I like breaking ground because that's when your idea becomes reality.

Blueprint: What new Coop Himmelb(l)au project excites you most?Prix: We just finished (the Musée des Confluences at) Lyon, the most complex building until now. It has an elaborated sculpture of water turbulence (the Gravity Well), 15m high. We are working on (something) similar in China 60m high (in the Dawang Mountain Resort, Changsha).

Blueprint: President Xi Jinping called for 'no more weird architecture' in China. Is that bad news for your Beijing office?Prix: The architectural profession is going down. There are too many architects. We are sardines in an ocean of sharks. The difference is, we don't have a swarm intelligence.

The 220m-long, 60m-high Dalian Conference Center, with a fluid envelope of steel, contains a conference and opera theatre

Blueprint: Are the sharks the clients?Prix: Clients always envy the starchitects because they have less pressure. They're wrong.

Blueprint: Perhaps Xi feels Western architects have used China as an experimental lab, for ever more digitised design.Prix: They have learnt a lot from these experiments. Xi is not trained in architecture. Digitisation itself is not a problem. Now, we are doing a project in China that is being built by robots (the Dolphin sculptured hub between MOCAPE's two museums, under construction in Shenzhen).

Blueprint: If you met your young self and said you were designing a headquarters for Europe's reserve bank, what do you think he would say?Prix: He'd say 'let's do it!' The difference is time, the attitude is the same.

Blueprint: And what advice would you give young architects?Prix: Don't fragment your power on stupid competitions or stupid buildings. You won't get results, (but) the client gets stronger. Go back to school and start a new wave of architectural thinking. Be independent from money and shark-like investors. Create a wave, learn to be patient.

Blueprint: But they need to pay the rentPrix: When we were young and refused a commission, we sold bananas, we drove trucks.

Blueprint: They may become just paper architects?Prix: It's not said that everyone should build. Sometimes a small sketch is more influential. If you only think in architectural terms, only architecture will come up. Architects now suffer from obedience before it's necessary.